Absolutely - it is nothing like a shower. Your skin releases sweat and your airways clear up because you breathe the hot air in and out. As you sit there and wait, your mind calms down too, much like it would during a proper work out.
A sauna visit warms you up down to the core especially in a cold winter climate. For several hours afterwards you feel warm, even when out about in the cold. It’s like that nice hot feeling after a shower sticks around for several hours instead of half an hour.
The shower is higher humidity though, and the hot water makes direct contact, so the heat is more conductive. Similar for a steam sauna, they are more potent at the same temperature. Also infrared saunas, but for a different reason (the light is absorbed directly into the tissue, without needing to heat the air). So it's definitely not just about temperature.
I can definitely turn my shower up for a hotter body experience than any sauna I've ever been in, and obviously it's nowhere near 150-195 which would be lethal.
Because the water is making direct contact with my body for much more heat transfer. The dry air of a sauna is vastly slower, plus you're sweating which provides evaporative cooling which isn't happening in the shower.
So I too really don't see how saunas are appreciably different from hot showers here.